The present invention relates to a method for predicting, by use of a silicon wafer, the density of micro crystal defects which may be produced when a silicon semiconductor element is formed from the silicon wafer, and an infrared absorption measurement apparatus used for embodying the method.
A substrate used in the manufacture of a silicon semiconductor element, i.e., a wafer, is normally prepared by the Czochralsky (CZ) method. A silicon wafer prepared by the CZ method contains about 10.sup.18 atoms/cm.sup.3 of oxygen, and almost all oxygen atoms (about 95%) are located between lattices. These interstitial oxygen atoms are infrared active, and absorb incident infrared rays. An infrared absorption spectrum obtained by irradiating infrared rays on the wafer has a peak absorption coefficient of 30 cm.sup.-1 and a half-value width of 36 cm.sup.-1 at a frequency corresponding to wave-numbers of 1106 cm.sup.-1 at room temperature. An absorption coefficient .alpha.1106 at this peak is proportional to the oxygen concentration of the wafer over a wide range.
Oxygen atoms contained in the silicon wafer in an oversaturation state are precipitated when the wafer is subjected to a thermal treatment during the manufacture of the semiconductor element, thus causing micro crystal defects. When these defects appear on an element-forming region of the wafer, the yield of the properly manufactured semiconductor elements is considerably reduced.
For this reason, conventionally, the oxygen concentration of wafers is specified in accordance with the manufacturing processes of semiconductor elements, and wafers having an oxygen concentration within a specified range are selected for the manufacture of semiconductor elements. Oxygen concentration [Oi] is calculated from the following equation and absorption coefficient .alpha.1106 measured as a monitor of an oxygen concentration by an infrared absorption method: EQU [Oi]=3.01.times.10.sup.17 .times..alpha.1106 atoms/cm.sup.3
However, when a plurality of wafers having the same oxygen concentration [Oi] are subjected to identical processes, the resulting micro crystal defect compositions cannot always be the same. For example, if a plurality of wafers, whose oxygen concentration is selected to fall within the range of 7 to 10.times.10.sup.17 cm.sup.-3, are subjected to an identical thermal treatment, a micro crystal defect density after the thermal treatment varies over the range of 10.sup.7 to 10.sup.10 cm.sup.-3 for each wafer.
Micro crystal defects are greatly influenced by residual carbon in the wafer. Normal wafers prepared by the CZ method contain an amount (&lt;2.times.10.sup.16 cm.sup.-3) of carbon which cannot be detected by the infrared absorption method. Nevertheless, the micro crystal defects cannot yet be controlled. For this reason, condition management during crystal growth and during manufacture, e.g., management of stability of a solid/liquid interface and thermal hysteresis, must be strictly performed. Therefore, the manufacture of semiconductor elements requires time and cost.